President Donald Trump just lobbed a ticking immigration time bomb at Capitol Hill with his decision to leave the fate of 800,000 so-called Dreamers in limbo — and lawmakers have no idea how they’ll defuse it.

House Republican leaders, already scrambling to avoid a government shutdown and a default on the nation’s debt, are privately hoping to push the immigration battle until at least this winter. They, like the White House, want a down payment on Trump’s border wall with Mexico in exchange for codifying the Deferred Action for Childhood Arrivals program — though House Democrats won’t say whether they’d accept tougher immigration restrictions in order to save it.

Meanwhile, Sens. Dick Durbin (D-Ill.) and Lindsey Graham (R-S.C.), longtime immigration-reform advocates, on Tuesday urged Congress to take up a DACA fix this month. But the Senate’s second-ranking Republican quickly dismissed that possibility.

“There’s no way,” Senate Majority Whip John Cornyn of Texas said of taking up Dreamer legislation in September. “We will take that up. I’m confident. But there’s no way that it will stand alone.”

“I think by and large, if you were able to have a stand-alone vote on a good product, [you] could pass it,” Rubio, a member of the bipartisan “Gang of Eight” that crafted a sweeping immigration bill four years ago, said in an interview with POLITICO. “If you start adding other things to it, that’s where I think it falls apart.”

The political and policy hurdles cast doubt on the prospects of salvaging DACA. Congress has struggled mightily with comprehensive immigration reform under multiple presidential administrations, in less polarized times.

The White House signaled that Trump would not be willing to sign a bill that deals solely with DACA. “We can’t just have one tweak to the system,” press secretary Sarah Huckabee Sanders said Tuesday.

Another senior administration official said the White House is hoping to win concessions on the border wall, more immigration enforcement agents or new restrictions to legal immigration. The Domestic Policy Council, which reports to White House immigration hard-liner Stephen Miller, plans to outline immigration policy goals and send them to Capitol Hill Republicans to guide negotiations, the source said.

“The bottom line of it is, I don’t think DACA as a clean bill can get through the Congress by itself,” Grassley said in a call with agriculture reporters on Tuesday. Grassley said it was an “opportunity for compromise between people that want DACA plus a lot of other things dealing with legal immigration, and I suppose even some things dealing with illegal immigration, that can probably be packaged together.”

Grassley spoke privately with California Sen. Dianne Feinstein, the top Democrat on the Judiciary Committee, about the prospects of taking up a legislative DACA fix through the panel, she said.

“He didn’t say no,” Feinstein said of Grassley’s reaction.

In the House, GOP leaders and senior Republicans are wary of any stand-alone bill extending DACA without concessions from Democrats — or cover from Trump. Speaker Paul Ryan (R-Wis.) urged Trump on Friday not to end the program, expressing concerns about how it would affect undocumented immigrants who came to the country as minors.

Multiple pro-DACA House and Senate sources have speculated that a legislative fix for Dreamers could pass the House with support from Democrats and moderate Republicans. But Ryan would take serious heat from conservatives if he were to allow that without getting anything in return.

That’s why Republican leaders, working with the White House, will likely seek a narrow deal that would extend the program while adopting some of Trump’s signature campaign promises on immigration.

At the top of the list: a down payment on Trump’s border wall with Mexico. Other options included changes to visa programs or other immigration policies aimed at tightening migration to the U.S. and movement across the border.

“If [Trump] gets involved, then the people in the House are going to fall in line,” said Graham, who is pushing legislation with Durbin that would give a pathway to green cards and ultimately citizenship for qualifying Dreamers. “The Senate won’t be your problem. The problem will be in the House.”

Graham was bullish about the prospects of a DACA fix in the Senate, saying, “I think the concept has 60 votes, yeah.”

Still, House Republican leaders appear to be in no rush to do anything immediately. Multiple senior sources speculated that a deal could be part of a bigger deal to raise spending caps later in December, or even a stand-alone bill after that.

Whenever it occurs and whatever it looks like, House Republicans will need Trump to give any deal his blessing — otherwise, immigration hawks in Ryan’s conference will rebel.

“It is my hope that the House and Senate, with the president’s leadership, will be able to find consensus on a permanent legislative solution that includes ensuring that those who have done nothing wrong can still contribute as a valued part of this great country,” Ryan said Tuesday in a statement that said nothing about how he plans to address the matter.

“President Obama wrongly believed he had the authority to re-write our immigration law. Today’s action by President Trump corrects that fundamental mistake,” McConnell said in his own statement after the decision. “This Congress will continue working on securing our border and ensuring a lawful system of immigration that works.”

Cornyn did express sympathy for the class of immigrants, saying “these children who were brought here illegally through no fault of their own continue to make positive contributions to Texas and the nation.”

For now, Democrats are insisting that DACA be handled on its own. House Democrats want to see a stand-alone DACA fix this month, House Minority Whip Steny Hoyer of Maryland told reporters Tuesday.

But Democrats, happy to keep the spotlight on the Republican response to Trump’s decision to end the program, aren’t threatening to withhold their support for other must-pass bills this month in exchange for a DACA fix — at least not yet.

“I’m going to keep my powder pretty dry at this point in time,” Hoyer said. “I’m not going to get into it in the next few days because I want to see what the Republicans do. I would hope they would do the responsible thing and the right thing.”

Democrats, long advocates for raising the debt ceiling without strings attached, are loath to be seen as hypocrites if they refuse to vote to lift the nation’s borrowing limit without a DACA solution in place.

But Hoyer acknowledged that with Democratic votes likely necessary to raise the debt ceiling and keep the government open later this month, Democrats may lose leverage on DACA the longer Congress waits to act.

Said Graham on Tuesday: “To the Dream Act population, there are a lot of people on the Republican side of the aisle [who] understand your dilemma. The only thing that stands between you and certainty in your life is the Congress. That cannot be that reassuring.”